They do mean slightly different things although they can be used, as in the original post, to mean the same thing.
Afterwards indicates that a specific event has occurred after another specific event.
"We are going to the movies and afterwards we are going out to eat."
If you want string events together in this structure you would do it like this:
"We are going to the movies and afterwards to eat and after that to
the zoo and after that to play laser tag."
Later merely indicates that something is happening a point in time later then the current point in time. This can be tied to the order of specific events in the manner of afterwards:
"We are going to the movies and later we're going out to eat"
or it can show the relationship between an event/events and point in time:
"Later we're going out to eat."
You would string events together in this structure like this:
"Later we are going to the movies and even later we are going to
You cannot say, "Afterwards we are going out to eat," because the listener needs to know, "After what?"